Width-adjustable wide-frequency-domain acoustic waveguide based on interval coupling type topological boundary state

Abstract

The invention discloses a width-adjustable wide-frequency-domain acoustic waveguide based on an interval coupling type topological boundary state, and belongs to the technical field of topological photonic crystals. The acoustic waveguide comprises interval coupling type topological boundary state scatterers and a substrate, and is characterized in that the interval coupling type topological boundary state scatterers are all arranged on the substrate; the periodically arranged scatterers form a cellular array, the scatterers are divided into I-type photonic crystals PnC1 and II-type photonic crystals PnC2 according to the rotation angles of the scatterers, a plurality of topological paths are constructed by arranging the two photonic crystals in a spaced coupling mode, and the wide-frequency-domain acoustic waveguide with the adjustable width is achieved. The width-adjustable acoustic waveguide is realized by introducing a plurality of topological paths, and low-loss, high-efficiency and wide-frequency-domain unidirectional transmission of acoustic wave signals along the topological paths is finally realized. The waveguide has high robustness and width adjustability, and a new thought is provided for solving the problem of connection between a topological structure and block equipment.

Description

Technical Field

[0001] The present invention belongs to the technical field of topological phononic crystals, and in particular relates to a wide-band acoustic waveguide with adjustable width based on interval-coupled topological boundary states. Background Art

[0002] When electrons are confined to two dimensions and exposed to strong magnetic fields, they exhibit a completely different topological order, which is the basis of the quantum Hall effect. This topological order also appears in certain three-dimensional materials, namely topological insulators. These materials are insulators in the bulk, but have exotic metallic states on their surfaces due to topological order. Acoustic topological insulators, similar to electronic topological insulators, have attracted great research interest from scholars. The edge states of acoustic topological insulators have remarkable propagation properties, especially defect immunity and backscattering suppression. As a result, research on acoustic topological insulators has revealed a variety of promising applications, such as backscatter-immune waveguides, topological frequency division multiplexing, topological cross-channels, and large-area waveguide states.

[0003] In the extensive research of condensed matter physics, people have proposed a method to guide wave energy using topological edge states. The topological phases of topological PnCs are usually distinguished by topological invariants. In topological systems, topological invariants can be characterized by Chern numbers. When two topological PnCs with different Chern numbers form an interface, according to the topological body-edge correspondence principle, a topologically protected edge state with robust properties will be generated. This edge state is immune to structural defects and impurities. This method has excellent advantages such as efficient energy transmission and no influence from defects, and has broad application prospects. However, waveguides based on topological edge states usually lack width adjustability. Recent studies have revealed a topological waveguide with width freedom. By intercalating PnCs containing degenerate points (B-type phononic crystals) between two PnCs with different topological phases (A- and C-type PnCs), an ABC heterostructure is formed. The large-area waveguide formed in this structure not only has excellent robustness and width adjustability, but also further improves the energy transmission efficiency.

[0004] Topological waveguides with adjustable width provide a new degree of freedom for acoustic wave control. However, the current method of realizing adjustable width waveguides based on ABC heterostructures faces limitations in the operating frequency band. Specifically, as the number of layers in the middle region (B-type PnC) gradually increases, the effective operating frequency band of the waveguide state will gradually narrow until it eventually disappears. This limits the practical application of topological waveguides with width freedom under the ABC structure. It can be seen that it is particularly urgent to design an acoustic waveguide with adjustable width whose operating frequency band is not limited by the waveguide width (number of layers in the middle region) and has good robustness. Summary of the invention

[0005] To solve the above problems, the present invention discloses a wide-band acoustic waveguide with adjustable width based on interval-coupled topological boundary states, which has the characteristics of adjustable energy transmission path width, strong robustness, unidirectional transmission, and efficient transmission, and is used to solve the connection problem between acoustic topological boundary states and bulk devices.

[0006] The above technical objectives of the present invention are achieved through the following technical solutions:

[0007] A width-adjustable wide-band acoustic waveguide based on an interval-coupled topological boundary state comprises an interval-coupled topological boundary state scatterer and a substrate, wherein the scatterers are all arranged on the substrate, and the bottom is connected to the substrate;

[0008] Every four adjacent scatterers form a unit cell, which is a type I phononic crystal PnC1; the scatterers are rotated 40 degrees counterclockwise around the center of the unit cell to form a type II phononic crystal PnC2. The two types of phononic crystals have different topological properties.

[0009] The present invention is further configured such that both type I phononic crystals and type II phononic crystals have C4 symmetry.

[0010] The present invention is further configured as follows: both type I phononic crystal PnC1 and type II phononic crystal PnC2 are tetragonal lattices with a lattice constant of a=64 mm, and each scatterer in the lattice is a fan ring with an outer radius of R=27.2 mm, an inner radius of r=25.8 mm, and a center angle of β=110°.

[0011] The present invention is further configured as follows: a finite rectangular acoustic structure is formed by combining a plurality of type I phononic crystals PnC1 and a plurality of type II phononic crystals PnC2.

[0012] The present invention is further configured as follows: the left and right sides of the finite rectangular acoustic structure are composed of a plurality of type I phononic crystals PnC1 or a plurality of type II phononic crystals PnC2, and the middle part is composed of type I phononic crystals PnC1 and type II phononic crystals PnC2 alternating in columns.

[0013] By applying an acoustic signal with a frequency of 2.9-3.2kHz below the acoustic structure, non-reciprocal transmission of a wide-channel acoustic waveguide can be achieved; the frequency of the designed phononic crystal unit cell only represents one case, and in actual applications, the phononic crystal unit cell needs to be designed according to the frequency band required by the actual working conditions.

[0014] The present invention is further configured such that the mutual conversion between type I phononic crystal PnC1 and type II phononic crystal PnC2 can be achieved by changing the rotation angle of the scatterer, thereby realizing an acoustic waveguide with adjustable width.

[0015] The present invention provides a wide-band acoustic waveguide with adjustable width based on interval-coupled topological boundary states according to the basic theory of topological phononic crystals. The acoustic waveguide of the present invention is suitable for the kHz frequency band and has a working bandwidth of hundreds of Hz. By adjusting the rotation angle of the phononic crystal scatterer in the middle part of the acoustic structure, multiple topological boundary states can be conveniently constructed in the structure to realize an acoustic topological waveguide with adjustable width.

[0016] The numerical simulation and experimentally measured acoustic field distribution both show that the proposed structure can not only realize an acoustic waveguide with adjustable mode width, but also has high transmission efficiency and robustness. Therefore, the present invention provides a potential solution to the problem of connecting topological boundary states with bulk devices in existing systems, and is helpful for the design and implementation of acoustic devices based on acoustic topological insulator theory.

[0017] The beneficial effects of the present invention are:

[0018] 1. The acoustic waveguide structure described in the present invention is novel in design, easy to manufacture, light in weight and low in cost; it ensures that the topological waveguide structure has the characteristics of high efficiency, low loss and flexible adjustability.

[0019] 2. Compared with other acoustic topological structures, the structure described in the present invention has a wider operating frequency band, and the operating bandwidth will not become narrower due to the increase in waveguide width. Efficient and robust sound transmission can be achieved within its operating frequency band.

[0020] 3. The acoustic waveguide structure described in the present invention realizes the adjustability of the waveguide width, which helps to solve the connection problem between the acoustic topological structure and the bulk device, and has great application prospects in the fields of acoustic sensing, acoustic energy collection, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A schematic diagram of a wide-band acoustic waveguide with adjustable width based on interval-coupled topological boundary states and its structural dimensions in an embodiment of the present invention;

[0022] Figure 2 Schematic diagram of the energy band structure of the acoustic waveguide with adjustable width according to an embodiment of the present invention; the upper and lower shaded areas in the energy band diagram are body states, the middle rectangular shaded area is the body energy band gap, and the dots within the band gap range represent topologically protected boundary states;

[0023] Figure 3 The acoustic field distribution diagram of the adjustable width acoustic waveguide according to the embodiment of the present invention at a frequency of 3.1kHz; (a) is when the number of layers in the middle region is 1, (b) is when the number of layers in the middle region is 5, and (c) is when the number of layers in the middle region is 13. The upper part of the figure is a schematic diagram of the waveguide structure, and the lower part of the figure is the acoustic field distribution;

[0024] Figure 4The acoustic field distribution diagram corresponding to a frequency of 3.1kHz when there is a defect in the acoustic waveguide with adjustable width described in an embodiment of the present invention; (a) is when the number of layers in the middle region is 1, (b) is when the number of layers in the middle region is 5, and (c) is when the number of layers in the middle region is 13. The upper part of the figure is a schematic diagram of the waveguide structure, and the lower part of the figure is the acoustic field distribution;

[0025] Figure 5 The transmittance variation curves of the acoustic waveguide with adjustable width according to the embodiment of the present invention in the complete and defective conditions as a function of frequency; (a) is when the number of layers in the middle region is 1, (b) is when the number of layers in the middle region is 5, and (c) is when the number of layers in the middle region is 13;

[0026] Figure 6 The curve of the working frequency band of the adjustable-width acoustic waveguide according to the embodiment of the present invention changing with the waveguide width. The shaded part represents the frequency range covered by the working frequency band of the waveguide. DETAILED DESCRIPTION

[0027] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0028] This embodiment provides a width-adjustable broadband acoustic waveguide based on interval-coupled topological boundary states, such as Figure 1 As shown, it includes a scatterer and a substrate, and the scatterers are all arranged on the substrate, and the bottom is connected to the substrate. Each phononic crystal contains 4 fan-shaped ring scatterers, and the shape formed by the 4 scatterers has C4 symmetry. The energy band can be reversed by rotating the scatterers around the center of the cell. The type I phononic crystal PnC1 is rotated 40 degrees counterclockwise to obtain the type II phononic crystal PnC2. The two types of phononic crystals have different topological properties, and there is a topologically protected boundary state at the interface of the two phononic crystals.

[0029] Among them, type I phononic crystal PnC1 and type II phononic crystal PnC2 are both tetragonal lattices with lattice constant a=64mm. The outer circle radius of each fan-shaped scatterer in the lattice is R=27.2mm, the inner circle radius is r=25.8mm, and the center angle is β=110°.

[0030] The left and right sides of the adjustable-width acoustic waveguide are composed of several I-type phononic crystals PnC1, and the middle part is composed of I-type phononic crystals PnC1 and II-type phononic crystals PnC2 alternating in columns. There are topologically protected boundary states on the domain walls of I-type phononic crystals PnC1 and II-type phononic crystals PnC2. There are 12 domain walls of I-type phononic crystals PnC1 and II-type phononic crystals PnC2 in the middle area of ​​the structure, providing 12 paths for the transmission of acoustic energy, thereby widening the width of the topological waveguide.

[0031] Figure 2 The schematic diagram of the band structure of the acoustic waveguide with adjustable width described in the embodiment of the present invention. Taking x=0 as the reference, 5 PnC1s are placed in sequence along the positive direction of the x-axis, and then 6 PnC2s and 5 PnC1s are placed alternately, and then 5 PnC1s are placed. Thus, a supercell containing 21 cells is formed, and the projection energy bands of the two PnCs along the y direction are calculated using the supercell calculation method to determine the boundary state. COMSOL Multiphysics software based on the finite element method is used for numerical simulation to calculate the energy band diagram of the supercell, and the periodic boundary conditions are applied to the upper and lower boundaries of the supercell, and the continuous boundary conditions are applied to the left and right boundaries of the supercell. The shaded areas in the upper and lower parts represent the body state, the rectangular shaded area represents the body energy band gap of the supercell, and the dots represent the dispersion curves of the boundary state. In order to more vividly characterize the topological boundary state, the figure on the right shows the acoustic field distribution of the two boundary states. The right 1 shows the eigenmode with a frequency of 2.99kHz and a wave vector of 1.01 (π / a), and the right 2 shows the eigenmode with a frequency of 3.10kHz and a wave vector of 1.4 (π / a).

[0032] In order to intuitively illustrate the transmission characteristics of the acoustic waveguide signal, the acoustic field distribution and transmittance curve of the acoustic waveguide with adjustable width described in the embodiment are simulated, and the sound wave propagation is shown in Figures 3 to 5 middle.

[0033] Figure 3 The sound intensity distribution of the acoustic waveguide when the sound wave with a frequency of 3.1kHz is incident from directly below the structure when the number of layers in the middle region is 1, 5, and 13 respectively. The number of layers in the middle region directly affects the width of the waveguide, and the sound energy is highly localized in the designed waveguide channel, which can well realize waveguides of different widths. Since the conversion between type I phononic crystal PnC1 and type II phononic crystal PnC2 can be realized by changing the rotation angle of the scatterer in the unit cell, the number of layers in the middle region can be changed by adjusting the rotation angle of the scatterer, thereby realizing an acoustic waveguide with adjustable width.

[0034] The most significant feature of topological waveguides is their immunity to structural defects. In order to verify the immunity of the proposed acoustic waveguide with adjustable width to structural defects, we removed a single lattice from the structure to form a lattice defect and calculated the acoustic field distribution of the waveguide in the presence of defects. Figure 4 The acoustic intensity distribution of the acoustic waveguide is shown when a sound wave with a frequency of 3.1 kHz is incident from directly below the structure containing defects when the number of layers in the middle region is 1, 5, and 13. It can be seen that at the current frequency, an acoustic waveguide with adjustable width can be realized even if there are defects in the structure.

[0035] To further demonstrate the acoustic wave transmission performance of acoustic waveguides with different widths in intact and defective conditions, Figure 5 (a)-(c) show the transmittance curves when the waveguide is complete and contains defects when the number of layers in the middle region of the structure is 1, 5, and 13 respectively. The shaded part in the figure is the working frequency band of the topological acoustic waveguide, which is obtained by calculating the band structure of the supercell. It can be seen from the transmittance curve that when the number of layers in the middle region is 1, the energy transmission efficiency of the topological acoustic waveguide is limited, the working bandwidth is narrow, and the transmission curve is greatly affected by defects. As the number of layers in the middle region increases, the energy transmission efficiency and robustness of the acoustic waveguide are significantly improved, and the working bandwidth of the waveguide is also significantly increased.

[0036] Figure 6 The curve of the working frequency band of the acoustic waveguide with adjustable width described in the embodiment of the present invention as the waveguide width changes is shown. The shaded part represents the frequency range covered by the working frequency band of the waveguide. It can be seen that when the number of layers in the middle region is 1, the working frequency range of the waveguide is 2958.5-3148.7Hz (bandwidth Δf=190.2Hz); when the number of layers in the middle region is 3, the working frequency range of the waveguide is 2911.2-3151.7Hz (Δf=240.5Hz); when the number of layers in the middle region is 13, the working frequency range of the waveguide is 2895.1-3200.5Hz (Δf=305.4Hz). Compared with the existing method of realizing adjustable width waveguide based on ABC heterostructure, the adjustable width acoustic waveguide described in the embodiment of the present invention effectively solves the limitation of its working bandwidth, that is, the working bandwidth of the adjustable width acoustic waveguide described in the embodiment of the present invention does not narrow due to the increase of the width of the waveguide.

[0037] The width-adjustable acoustic waveguide based on topological boundary states described in the embodiment of the present invention realizes the width-adjustable acoustic waveguide by adjusting the rotation angle of the scatterer to construct multiple energy transmission channels in the structure. It is verified by the embodiment that the proposed width-adjustable acoustic waveguide has the characteristics of high transmission efficiency, strong robustness, good working bandwidth, etc., which shows a broad prospect for the practical application of waveguides based on topological insulators. The present invention is conducive to solving the connection problem between topological devices and bulk devices, and provides the possibility of designing broadband, multifunctional, strong robustness and highly flexible topological devices.

[0038] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above technical features.

Claims

1. A width-adjustable broadband acoustic waveguide based on interval-coupled topological boundary states, characterized in that: It comprises an interval-coupled topological boundary state scatterer and a substrate. The scatterer is arranged on the substrate, and the bottom is connected to the substrate.

2. According to claim 1, a width-adjustable wide-band acoustic waveguide based on interval-coupled topological boundary states is characterized in that: Every four adjacent scatterers form a unit cell, which is a type I phononic crystal PnC1. The scatterers are rotated 40 degrees counterclockwise around the center of the unit cell to form a type II phononic crystal PnC2. Type I phononic crystal PnC1 and type II phononic crystal PnC2 have different topological properties.

3. The width-adjustable wide-band acoustic waveguide based on interval-coupled topological boundary states according to claim 2, characterized in that: Both type I phononic crystal PnC1 and type II phononic crystal PnC2 have C4 symmetry.

4. The width-adjustable broadband acoustic waveguide based on interval-coupled topological boundary states according to claim 2, characterized in that: Both type I phononic crystal PnC1 and type II phononic crystal PnC2 are tetragonal lattices with a lattice constant of a=64 mm. Each scatterer in the lattice is a fan ring with an outer radius of R=27.2 mm, an inner radius of r=25.8 mm, and a center angle of α=110°.

5. The width-adjustable broadband acoustic waveguide based on interval-coupled topological boundary states according to claim 2, characterized in that: A finite rectangular acoustic structure is formed by combining a number of type I phononic crystals PnC1 and a number of type II phononic crystals PnC2.

6. The width-adjustable broadband acoustic waveguide based on interval-coupled topological boundary states according to claim 4, characterized in that: The left and right sides of the finite rectangular acoustic structure are composed of a plurality of type I phononic crystals PnC1 or a plurality of type II phononic crystals PnC2, and the middle part is composed of type I phononic crystals PnC1 and type II phononic crystals PnC2 alternately in columns.

7. The width-adjustable wide-band acoustic waveguide based on interval-coupled topological boundary states according to claim 5, characterized in that: By applying an acoustic signal with a frequency of 2.9-3.2kHz under the acoustic structure, non-reciprocal transmission of a wide-channel acoustic waveguide can be achieved; the frequency of the designed phononic crystal unit cell only represents one case, and in actual applications, the phononic crystal unit cell needs to be designed according to the frequency band required by the actual working conditions.

8. The width-adjustable wide-band acoustic waveguide based on interval-coupled topological boundary states according to claim 6, characterized in that: By changing the rotation angle of the scatterer, the mutual conversion between type I phononic crystal PnC1 and type II phononic crystal PnC2 can be achieved, and an acoustic waveguide with adjustable width can be realized.

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